Breaking the first rule

There's one aspect of the bull market in gilts that hasn't had the attention it deserves - the fact that it is undermining the first rule of finance - the one that says higher risk should mean higher expected returns.

But for a long time now, safer assets have done better than risky ones. Over the last 20 years, total returns on gilts have averaged 0.5 percentage points a year more than total returns (including dividends) on equities.

The first rule of finance, then, is broken. Why?

One possibility is mere bad luck. High risk only means high return if risks do not materialise. But in recent years they have. It's possible, then, that the rule is correct and we've just been unlucky.

In fact, such is the volatility of shares that even 20 years is too small a sample from which to infer anything robust about returns. Since June 1992 the standard deviation of returns on equities relative to gilts has been 16.8 percentage points. This implies that the standard error around the observed 0.5 percentage point outperformance by gilts is 3.8 percentage points. This means that it's perfectly possible that the true return on equities is higher than that on gilts and the last 20 years have just been an unlucky sample. Christian Lundblad of the University of North Carolina has pointed out that if we take a sample long enough to permit robust inference, then there is indeed a normal relationship between risk and return.

However, the outperformance of gilts over equities is not the only evidence that high risk goes unrewarded and that safety pays. There are at least four other facts that contradict the first rule of finance:

■ Defensive stocks outperform more volatile ones around the world and over the long term

■ For half of the year (May to September), the All-Share index has on average underperformed cash.

■ Facebook's share price fall reminds us that newly-issued shares underperform on average. This is despite the fact that their lack of public track record means they should be riskier than more seasoned shares.

■ John Campbell at Harvard University has found that shares in companies on the brink of bankruptcy tend on average to underperform the market, despite their obvious riskiness.

It is unlikely that all these facts are just an artefact of the great noise surrounding returns. We should therefore consider why it might be that high risk isn't, on average, associated with high return.

One reason could simply be that investors' cognitive biases cause them to underestimate risk and overestimate return. The pursuit of glamorous growth stocks causes them to be overpriced relative to dull defensives, with the result that the latter outperform over the long run. The impulses towards overreaction and herding generate bubbles in risky assets, the bursting of which causes years of underperformance. And investors' limited attention means they are attracted to volatile stocks simply because these have more newsflow than dull defensives which tend to stay under the radar - which again causes risky stocks to be overpriced.

Another reason why risk might not be rewarded could simply be that investors are not averse to it. Elementary theory says that people hate risk and so tend to avoid assets that carry it, causing such assets to be priced low enough to offer high subsequent returns. But people don't always hate risk; the ubiquity of casinos, bookies and online gambling tells us as much. And prospect theory tells us that when people have made a loss they are tempted to gamble in an effort to get even. To the extent that people like to bet on risky assets, their returns should be low - just as the average returns to punters in bookies and casinos is low.

We shouldn't dismiss this possibility. Nardin Baker of Guggenheim Investments says fund managers might be risk-seeking, in the sense of preferring volatile stocks, because these offer the chance of big outperformance in normal times when the market rises. And such outperformance not only boosts their egos, but also their salaries to the extent that investors tend to buy previously good-performing funds.

Eric Falkenstein, author of Finding Alpha, has another explanation for why risk doesn't bring higher return. If investors care about relative returns rather than absolute ones, he says, then all assets are risky. 'Safe' assets - be they bonds or defensive stocks - carry the risk of underperforming in good times while risky assets risk underperforming in bad times. To someone concerned with their wealth relative to others, both risks are to be avoided. The risk premium of 'safe' assets should then be equal to that on risky assets - or even higher, if good times are more likely than bad.

Such positional concerns are certainly strong for professional fund managers; a return of 10 per cent when his rivals are making 20 per cent could cost a manager his job. But they might also matter for private investors. To the extent that we regard stock-picking as a test of our ability, then we fret about performance relative to the market rather than absolute performance, and we might seek out speculative shares that test our skills rather than defensive ones; how much skill does it take to buy National Grid?

Perhaps, then, the first rule of finance is wrong. There are reasons to suspect that risky assets will very often underperform safe ones.

All of this looks like yet another attack upon conventional economics. But it's more than that. If high risk doesn't mean high average returns then we have no good way of gauging expected returns. And this means that investors are at sea in uncharted waters - and perhaps in unchartable ones.

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